The present invention relates to ellipsometry and polarimetry, and more particularly is a system for focusing an electromagnetic beam as a small spot over a large range of wavelengths including into the deep UV, and further is a method for evaluating parameters in parameterized equations for calculating retardance entered to orthogonal components in a beam of electromagnetic radiation, by multiple element input and output lenses, through which said beam of electromagnetic radiation is caused to pass.
The practice of ellipsometry is well established as a non-destructive approach to determining characteristics of sample systems, which can be practiced in real time. The topic is well described in a number of publication, one such publication being a review paper by Collins, titled xe2x80x9cAutomatic Rotating Element Ellipsometers: Calibration, Operation and Real-Time Applicationsxe2x80x9d, Rev. Sci. Instrum, 61(8) (1990).
In general, the practice of ellipsometry typically involves causing a spectroscopic beam of electromagnetic radiation, in a known state of polarization, to interact with a sample system at some angle of incidence with respect to a normal to a surface thereof, in a plane of incidence. (Note, a plane of incidence contains both a normal to a surface of an investigated sample system and the locus of said beam of electromagnetic radiation). Changes in the polarization state of said beam of electromagnetic radiation which occur as a result of said interaction with said sample system are indicative of the structure and composition of said sample system. The practice of ellipsometry determines said changes in polarization state by proposing a mathematical model of the ellipsometer system and the sample system investigated by use thereof. Experimental data is then obtained by application of the ellipsometer system, and a square error reducing mathematical regression, (typically), is then applied to the end that parameters in the mathematical model which characterize the sample system are evaluated so that the obtained experimental data, and values calculated by use of the mathematical model are essentially identical.
A typical goal in ellipsometry is to obtain, for each wavelength in, and angle of incidence of said beam of electromagnetic radiation caused to interact with a sample system, sample system characterizing PSI and DELTA values, (where PSI is related to a change in a ratio of magnitudes of orthogonal components rp/rs in said beam of electromagnetic radiation, and wherein DELTA is related to a phase shift entered between said orthogonal components rp and rs, caused by interaction with said sample system;
PSI=|rp/rs|;
and
DELTA=∠rpxe2x88x92∠rs)).
As alluded to, the practice of ellipsometry requires that a mathematical model be derived and provided for a sample system and for the ellipsometer system being applied. In that light it must be appreciated that an ellipsometer system which is applied to investigate a sample system is, generally, sequentially comprised of:
a. a Source of a beam electromagnetic radiation;
b. a Polarizer element;
c. optionally a compensator element;
d. (additional element(s));
e. a sample system;
f. (additional element(s));
g. optionally a compensator element;
h. an Analyzer element; and
i. a Detector System.
Each of said components b.-i. must be accurately represented by a mathematical model of the ellipsometer system along with a vector which represents a beam of electromagnetic radiation provided from said source of a beam electromagnetic radiation, Identified in a. above)
Various ellipsometer configurations provide that a Polarizer, Analyzer and/or Compensator(s) can be rotated during data acquisition, and are describe variously as Rotating Polarizer (RAE), Rotating Analyzer (RAE) and Rotating Compensator (RCE) Ellipsometer Systems.
Where an ellipsometer system is applied to investigate a small region of a sample system present, it must be appreciated that the beam of electromagnetic radiation can be entered thereto through an converging input lens, and exit via a diverging output lens. In effect this adds said converging input and diverging output lenses as elements in the ellipsometer system as xe2x80x9cadditional elementsxe2x80x9d, (eg. identified in d. and f. above), which additional elements must be accounted for in the mathematical model. If this is not done, sample system representing parameters determined by application of the ellipsometer system will have the effects of said converging input and diverging output lenses at least partially correlated thereinto, much as if the converging input and diverging output lenses were integrally a part of the sample system.
It is further noted that where two sequentially adjacent elements in an ellipsometer system are held in a static position with respect to one another while experimental ellipsometric data is acquired, said two sequentially adjacent elements generally appear to be a single element. Hence, a beam directing element adjacent to a lens can appear indistinguishable from said lens as regards the overall effect of said combination of elements. In that light it is to be understood that converging input and diverging output lenses are normally structurally fixedly positioned and are not rotatable with respect to a sample system present in use, thus preventing breaking correlation between parameters in equations for sequentially adjacent converging input and diverging output lenses and an investigated sample system by an element rotation technique. While correlation of parameters in mathematical equations which describe the effects of groupings of elements, (such as a compensator and an optional element(s)), can be tollerable, correlation between parameters in the mathematical model of an investigated sample system and other elements in the ellipsometer system must be broken to allow obtaining accurate sample system representing PSI and DELTA values, emphasis added. That is to say that correlation between parameters in a equations in a mathematical model which describe the effects of a stationary compensator and a sequentially next lens element, (eg. correllation between effects of elements c. and d. or between f. and g. identified above), in a beam of electromagnetic radiation might be tolerated to the extent that said correlation does not influence determination of sample system describing PSI and DElTA values, but the correlation between parameters in equations which describe the effects of ellipsometer system components (eg. a., b., c., d., f., g., h. and i.), and equations which describe the effects of a present sample system (eg. element e. above), absolutely must be broken to allow the ellipsometer system to provide accurate PSI and DELTA values for said sample system. In-situ application of ellipsometry to investigation of a sample system present can then present a challenge to users of ellipsometer systems in the form of providing a mathematical model for each of a converging input and diverging output lens, and providing a method by which the effects of said converging input and diverging output lenses can be separated from the effects of an investigated sample system.
Thus is identified an example of a specific problem, solution of which is the topic of the present invention.
One typical approach to overcomming the identified problem, where space considerations are not critical, and where ellipsometer system configuration can be easily modified, is to obtain multiple data sets with an ellipsometer system configured differently during at least two different data set acquisitions. For instance, a data set can be obtained with a sample system present and in which a beam of electromagnetic radiation is caused to interact with said sample system, and another data set can be obtained with the ellipsometer system configured in a straight-through configuration, where a beam of electromagnetic radiation is caused to pass straight through an ellipsometer system without interacting with a sample system. Simultaneous mathematical regression utilizing both data sets can allow evaluation of sample system characterizing PSI and DELTA values over a range of wavelengths, uncorrelated with present bi-refringent retardation effects of said converging input and diverging output lenses. The problem with this approach is that where ellipsometer systems are fit to vacuum chambers for instance, ellipsometer reconfiguration so as to allow acquisition of such multiple data sets can be extremely difficult, if not impossible to carry out.
Another rather obvious solution to the identified problem is to provide converging input and diverging output lenses which are absolutely transparent at all electromagnetic beam wavelengths utilized. That is, provide converging input and diverging output lenses which do not attenuate the magnitude of rp or rs orthogonal components, (or at least do not change their ratio, rp/rs), and which also do not enter phase shift between rp or rs orthogonal components when said beam of electromagnetic radiation is caused to pass therethrough. While control of the the effect of a lens on a ratio, (rp/rs), of electromagnetic beam orthogonal components can often rather successfully be accomplished by causing a beam of electromagnetic radiation to approach a surface of a lens along a normal to a surface thereof, this is not the case regarding phase shift entered between rp and rs orthogonal components of a said beam of electromagnetic radiation caused to pass therethrough. That is, converging input and diverging output lenses can demonstrate xe2x80x9cbi-refringencexe2x80x9d, in that the rp orthogonal component is xe2x80x9cretardedxe2x80x9d by a different amount than is the rs orthogonal component when said beam of electromagnetic radiation is caused to pass therethrough. To complicate matters, this xe2x80x9cbi-refringentxe2x80x9d effect also varies with wavelength and with stresses which can develop in a lens during use because of temperature and physical changes etc.
As described in Co-pending application Ser. No. 09/162,217, (which is incorporated herein by reference), controlling stress related change is presently achieved with varying degrees of success, where for instance, windows in a vacuum chamber are subject. Windows provided by BOMCO Inc. are produced with the goal of eliminating bi-refringence, and are mounted in vacuum chambers using xe2x80x9cOxe2x80x9d ring seals which help to minimize uneven application of stresses and developed strains thereacross. While some success is achieved via this approach, the BOMCO windows are not xe2x80x9cperfectxe2x80x9d and do demonstrate some remaining bi-refringence properties, which can an vary in unpredictable ways over a period of usage. In addition, BOMCO windows are expensive, costing on the order of $1000.00 each), and are large in size thereby making adaptation thereof to use in a vacuum chamber difficult at times, particularly in retro-fit scenarios. And, there have been cases where BOMCO windows have broken in use. This is highly undesirable as vacuum chambers are often times caused to contain highly toxic and hazardous materials during, for instance, etching and/or deposition steps required in the fabrication of semiconductor devices. Where vacuum chamber windows are the subject, an alternative to use of the BOMCO windows is to simply use standard vacuum chamber windows, which, while significantly less expensive, demonstrate order of magnitude larger bi-refringence effects. (Note, BOMCO windows provide bi-refringent effects on the order of approximately six-tenths (0.6) to two-tenths (0.2) degrees over a range of wavelengths of from four-hundred (400) to seven-hundred-fifty (750) nanometers, whereas standard vacuum windows demonstrate birefringent effects on the order of six (6.0) to three (3.0) degrees over the same range of wavelengths). (Note, bi-refringent retardation typically follows an approximate inverse wavelength, (eg. 1/wavelength), relationship). However, where standard vacuum chamber windows are utilized, compensation of their effects is required. Similar concerns apply where converging input and diverging output lenses, and associated ellipsometrically indistinguishable ellipsometer system components are on point.
A need is thus identified for a method of practicing ellipsometry which enables the breaking of correlation between parameters in equations which describe retardance entered to orthogonal components of a beam of electromagnetic radiation caused to interact with a sample system, and parameters in equations which describe bi-refringent effects on said orthogonal components in said beam of electromagnetic radiation caused by input and output windows of a vacuum chamber, and/or by converging input and diverging output lenses etc.
Various researchers have previously noted the identified problem, where vacuum chamber windows are the topic, and proposed various first order mathematical model equation correction techniques as solution, which approaches have met with various degrees of success where vacuum chamber input and output windows demonstrate on the order of a maximum of two (2) degrees of bi-refringence. This, however, leaves the problem unsolved where bi-refringence approaches six (6.0) degrees, as commonly occures in standard vacuum chamber windows, and can also occur in lens systems, particlarly at wavelengths of four-hundred (400) nanometers and below.
Patents of which the Inventor is aware include U.S. Pat. No. 5,757,494 to Green et al., in which is taught a method for extending the range of Rotating Analyzer/Polarizer ellipsometer systems to allow measurement of DELTAS near zero (0.0) and one-hundred-eighty (180) degrees. Said Patent describes the presence of a window-like variable bi-refringent components which is added to a Rotating Analyzer/Polarizer ellipsometer system, and the application thereof during data acquisition, to enable the identified capability.
A Patent to Thompson et al. U.S. Pat. No. 5,706,212 teaches a mathematical regression based double fourier series ellipsometer calibration procedure for application, primarily, in calibrating ellipsometers system utilized in infrared wavelength range. Bi-refringent window-like compensators are described as present in the system thereof, and discussion of correlation of retardations entered by sequentially adjacent elements which do not rotate with respect to.one another during data acquisition is described therein.
A Patent to Woollam et al, U.S. Pat. No. 5,582,646 is disclosed as it describes obtaining ellipsometic data through windows in a vacuum chamber, utilizing other than a Brewster Angle of Incidence.
Patent to Woollam et al, U.S. Pat. No. 5,373,359, Patent to Johs et al. U.S. Pat. No. 5,666,201 and Patent to Green et al., U.S. Pat. No. 5,521,706, and Patent to Johs et al., U.S. Pat. No. 5,504,582 are disclosed for general information as they pertian to Rotating Analyzer ellipsometer systems.
Patents identified in a Search specifically focused on the use of lenses, preferrably achromatic, in ellipsometry and realted systems are:
U.S. Pat. Nos. 5,877,859 and 5,798,837 to Aspnes et al.;
U.S. Pat. No. 5,333,052 to Finarov;
U.S. Pat. No. 5,608,526 to Piwonka-Corle et al.;
U.S. Pat. No. 5,793,480 to Lacy et al.;
U.S. Pat. Nos. 4,636,075 and 4,893,932 to Knollenberg; and
U.S. Pat. No. 4,668,860 to Anthon.
A paper by Johs, titled xe2x80x9cRegression Calibration Method for Rotating Element Ellipsometersxe2x80x9d, Thin Solid Films, 234 (1993) is also disclosed as it describes a mathematical regression based approach to calibrating ellipsometer systems.
A paper by Nijs and Silfhout, titled xe2x80x9cSystematic and Ramdom Errors in Rotating-Analyzer Ellipsometryxe2x80x9d, J. Opt. Soc. Am. A., Vol. 5, No. 6, (June 1988), describes a first order mathematical correction factor approach to accounting for window effects in Rotating Analyzer ellipsometers.
A paper by Kleim et al, titled xe2x80x9cSystematic Errors in Rotating-Compensator ellipsometryxe2x80x9d, J. Opt. Soc. Am., Vol 11, No. 9, (September 1994) describes first order corrections for imperfections in windows and compensators in Rotating Compensator ellipsometers.
Principal component analysis and neural network approaches to the problem are discussed in a paper by Pickering et al, titled xe2x80x9cInstrumental and Computational Advances for Real-time Processes Control Using Spectroscopic Ellipsometryxe2x80x9d, Int. Conf. on Netrology and Charcterization for VSLI Tech., NIST, (March 1998).
Other papers of interest in the area by Azzam and Bashara include one titled xe2x80x9cUnified Analysis of Ellipsometry Erors Due to Imperfect Components Cell-Window Birifringence, and Incorrect Azimuth Anglesxe2x80x9d, J. of the Opt. Soc. Am., Vol 61, No. 5, (May 1971); and one titled xe2x80x9cAnalysis of Systematic Errors in Rotating-Analyzer Ellipsometersxe2x80x9d, J. of the Opt. Soc. Am., Vol. 64, No. 11, (November 1974).
Another paper by Straaher et al, titled xe2x80x9cThe Influence of Cell Window Imperfections on the Calibration and Measured Data of Two Types of Rotating Analyzer Ellipsometersxe2x80x9d, Surface Sci., North Holland, 96, (1980), describes a graphical method for determining a plane of incidence in the presence of windows with small retardation.
A paper by Jones titled xe2x80x9cA New Calculus For The Treatment Of Optical Systemsxe2x80x9d, J.O.S.A., Voil. 31, (July 1941), is also identified as it describes the characterizing of multiple lens elements as a single lens.
Finally, A paper which is co-authored by the inventor herein is titled xe2x80x9cIn Situ Multi-Wavelength Ellipsometric Control of Thickness and Composition of Bragg Reflector Structuresxe2x80x9d, by Herzinger, Johs, Reich, Carpenter and Van Hove, Mat. Res. Soc. Symp. Proc., Vol.406, (1996) is also disclosed.
In view of relevant prior art, and the inability of first order corrections to break correlation, there remains need for a second order mathematical model equation correction technique which enables breaking correlation between sample system characterization DELTA and in-plane retardance entered to a beam of electromagnetic radiation entered by converging input and diverging output lenses through which said beam of electromagnetic radiation is caused to pass. This is particularly true where lens bi-refringent retardance exceeds a few degrees, as and can be the case.
The present invention is primarily a method of accurately evaluating parameters in parameterized equations in a mathematical model of a system of spatially separated converging input and diverging output lenses, as applied in an ellipsometry or polarimetry setting. Said parameterized equations enable, when parameters therein are properly evaluated, independent calculation of retardation entered by each of said converging input lens and said diverging output lens between orthogonal components of a beam of electromagnetic radiation caused to pass through said converging input and diverging output lenses. (It is to be understood that at least one of said converging input and diverging output lenses is typically considered to be at least somewhat birefringent). In a basic sense, said method comprises, in a functional order, the steps of:
a. providing spatially separated converging input and diverging output lenses, at least one of said converging input diverging output lenses demonstrating birefringence when a beam of electromagnetic radiation is caused to pass therethrough, there being a means for supporting a sample system positioned between said converging input and diverging output lenses;
b. positioning an ellipsometer system source of electromagnetic radiation and an ellipsometer system detector system such that in use a beam of electromagnetic radiation provided by said source of electromagnetic radiation is caused to pass through said converging input lens, interact with said sample system in a plane of incidence thereto, and exit through said diverging output lens and enter said detector system;
c. providing a sample system to said means for supporting a sample system, the composition of said sample system being sufficiently well known so that retardance entered thereby to a polarized beam of electromagnetic radiation of a given wavelength, which is caused to interact with said sample system in a plane of incidence thereto, can be accurately modeled mathematically by a parameterized equation which, when parameters therein are properly evaluated, allows calculation of retardance entered thereby between orthogonal components of a beam of electromagnetic radiation caused to interact therewith in a plane of incidence thereto, given wavelength;
d. providing a mathematical model for said ellipsometer system and said converging input and diverging output lenses and said sample system, comprising separate parameterized equations for independently calculating retardance entered between orthogonal components of a beam of electromagnetic radiation caused to pass through each of said converging input and diverging output lenses and interact with said sample system in a plane of incidence thereto; such that where parameters in said mathematical model are properly evaluated, retardance entered between orthogonal components of a beam of electromagnetic radiation which passes through each of said converging input and diverging output lenses and interacts with said sample system in a plane of incidence thereto can be independently calculated from said parameterzed equations, given wavelength;
e. obtaining a spectroscopic set of ellipsometric data with said parameterizable sample system present on the means for supporting a sample system, utilizing a beam of electromagnetic radiation provided by said source of electromagnetic radiation, said beam of electromagnetic radiation being caused to pass through said converging input lens, interact with said parameterizable sample system in a plane of incidence thereto, and exit through said diverging output lens and enter said detector system;
f. by utilizing said mathematical model provided in step d. and said spectroscopic set of ellipsometric data obtained in step e., simultaneously evaluating parameters in said mathematical model parameterized equations for independently calculating retardance entered between orthogonal components in a beam of electromagnetic radiation caused to pass through said input converging lens, interact with said sample system in a plane of incidence thereto, and exit through said diverging output lens.
The end result of practice of said method is that application of said parameterized equations for each of said converging input lens, diverging output lens and sample system for which values of parameters therein have been determined in step f., enables independent calculation of retardance entered between orthogonal components of a beam of electromagnetic radiation by each of said converging input and diverging output lenses, and said sample system, at given wavelengths in said spectroscopic set of ellipsometric data. And, it is emphasized that said calculated retardance values for each of said converging input lens, output diverging lens and sample system are essentially uncorrelated.
As further discussed supra herein, a modification to the just recited method can be to, (in the step d. provision of a mathematical model for said ellipsometer system and said input and diverging output lenses and said parameterizable sample system for each of said converging input and diverging output lenses), provide separate parameterized mathematical model parameterized equations for retardance entered to each of said two orthogonal components of a beam of electromagnetic radiation caused to pass through said converging input and diverging output lenses. When this is done, at least one of said orthogonal components for each of said input converging and diverging output lenses is directed out of the plane of incidence of said electromagnetic beam onto said parameterizable sample system. And, typically, though not necessarily, one orthogonal component will be aligned with the plane of incidence of said electromagnetic beam onto said parameterizable sample system. When this is done, calculation of retardation entered between orthogonal components of said beam of electromagnetic radiation, given wavelength, by said input converging lens is provided by comparison of retardance entered to each of said orthogonal components for said converging input lens, and such that calculation of retardation entered between orthogonal components of said beam of electromagnetic radiation, given wavelength, by said diverging output lens is provided by comparison of retardance entered to each of said orthogonal components for said diverging output lens.
It is pointed out that the step f. simultaneous evaluation of parameters in said mathematical model parameterized equations for said parameterizable sample system, and for said converging input diverging output lenses, is typically, though not necessarily, achieved by a square error reducing mathematical curve fitting procedure.
It is important to understand that in the method recited infra, the step b. positioning of an ellipsometer system source of electromagnetic radiation and an ellipsometer system detector system includes positioning a polarizer between said source of electromagnetic radiation and said converging input lens, and the positioning of an analyzer between said diverging output lens and said detector system, and in which the step e. obtaining of a spectroscopic set of ellipsometric data typically involves obtaining data at a plurality of settings of at least one component selected from the group consisting of: (said analyzer and said polarizer). As well, it is to be understood that additional elements can also be placed between said source of electromagnetic radiation and said converging input lens, and/or between said diverging output lens and said detector system, and that the step e. obtaining of a spectroscopic set of ellipsometric data can involve, alternatively or in addition to the recited procedure, obtaining data at a plurality of settings of at least one of said additional components.
It is also to be understood that the step of providing separate parameterized mathematical model parameterized equations for enabling independent calculation of retardance entered by said converging input said diverging output lenses between orthogonal components of a beam of electromagnetic radiation caused to pass through said converging input and diverging output lenses, and by said sample system, preferably involves parameterized equations having a form selected from the group consisting of:
ret(xcex)=(K1/xcex)
ret(xcex)=(K1/xcex)*(1+(K2/xcex))
ret(xcex)=(K1/xcex)*(1+(K2/xcex)+(K3/xcex4))
A modified method of accurately evaluating parameters in parameterized equations in a mathematical model of a system of spatially separated converging input and diverging output lenses, said parameterized equations enabling, when parameters therein are properly evaluated, independent calculation of retardation entered by each of said input converging lens and said output lens to at least one orthogonal component(s)of a beam of electromagnetic radiation caused to pass through said converging input and diverging output lenses, at least one of said converging input and diverging output lenses being birefringent, said method comprising, in a functional order, the steps of:
a. providing spatially separated converging input and diverging output lenses, at least one of said converging input and diverging output lenses demonstrating birefringence when a beam of electromagnetic radiation is caused to pass therethrough, there being a means for supporting a sample system positioned between said converging input and diverging output lenses;
b. positioning an ellipsometer system source of electromagnetic radiation and an ellipsometer system detector system such that in use a beam of electromagnetic radiation provided by said source of electromagnetic radiation is caused to pass through said converging input lens, interact with said sample system in a plane of incidence thereto, and exit through said diverging output lens and enter said detector system;
c. providing a sample system to said means for supporting a sample system;
d. providing a mathematical model for said ellipsometer system and said converging input and diverging output lenses and said sample system, comprising, for each of said input converging lens and said diverging output lens, separate parameterized equations for retardance for at least one orthogonal component in a beam of electromagnetic radiation provided by said source of electromagnetic radiation, which orthogonal component is directed out of a plane of incidence which said electromagnetic beam makes with said sample system in use, and optionally providing separate parameterized equations for retardance for an in-plane orthogonal component of said beam of electromagnetic radiation, such that retardation entered to said out-of-plane orthogonal component, and optionally to said in-plane orthogonal component, of said beam of electromagnetic radiation by each of said converging input and diverging output lenses, can, for each of said converging input and diverging output lenses, be separately calculated by said parameterized equations, given wavelength, where parameters in said parameterized equations are properly evaluated;
e. obtaining a spectroscopic set of ellipsometric data with said sample system present on the means for supporting a sample system, utilizing a beam of electromagnetic radiation provided by said source of electromagnetic radiation, said beam of electromagnetic radiation being caused to pass through said input lens, interact with said sample system in a plane of incidence thereto, and exit through said diverging output lens and enter said detector system;
f. by utilizing said mathematical model provided in step d. and said spectroscopic set of ellipsometric data obtained in step e., simultaneously evaluating sample system DELTA""S in correlation with in-plane orthogonal component retardation entered to said beam of electromagnetic radiation by each of said input converging and diverging output lenses, and parameters in said mathematical model parameterized equations for out-of-plane retardance entered by said converging input lens and said output lens to a beam of electromagnetic radiation caused to pass through said input lens, interact with said sample system in said plane of incidence thereto, and exit through said output lens.
Again, application of said parameterized equations for out-of-plane retardance entered by said converging input lens and said diverging output lens to a beam of electromagnetic radiation caused to pass through said converging input lens, interact with said sample system in said plane of incidence thereto, and exit through said diverging output lens, for which values of parameters therein are determined in step f., enables independent calculation of retardance entered to said out-of-plane orthogonal component of a beam of electromagnetic radiation by each of said converging input and diverging output lenses, given wavelength.
Also, again the step f. simultaneous evaluation of parameters in said mathematical model parameterized equations for calculation of retardance entered to said out-of-plane orthogonal component of a beam of electromagnetic radiation by each of said converging input and diverging output lenses, given wavelength, and said correlated sample system DELTA""S and retardance entered to said in-plane orthogonal component of a beam of electromagnetic radiation by each of said input converging and diverging output lenses, is typically achieved by a square error reducing mathematical curve fitting procedure.
It remains, in the presently disclosed method, to provide values for parameters in the in-plane parameterized equations for retardation, in said mathematical model of a system of spatially separated converging input and diverging output lenses. The presently disclosed method threfore further comprises the steps of:
g. providing a parameterized equation for retardation entered by said sample system to the in-plane orthogonal component of a beam of electromagnetic radiation, and as necessary similar parameterized equations for retardation entered by each of said converging input and diverging output lenses to the in-plane orthogonal component of a beam of electromagnetic radiation; and
h. by utilizing said parameterized mathematical model provided in step d. and said spectroscopic set of ellipsometric data obtained in step e., simultaneously evaluating parameters in said mathematical model parameterized equations for independent calculation of retardance entered in-plane by said sample system and by said converging input lens and said diverging output lens such that the correlation between sample system DELTA""S and the retardance entered by said in-plane orthogonal component of a beam of electromagnetic radiation by each of said input converging and diverging output lenses, at given wavelengths in said spectroscopic set of ellipsometric data, is broken.
The end result of practice of the immediately foregoing steps a.-h. is that application of said parameterized equations for each of said converging input lens, diverging output lens and sample system for which values of parameters therein have been determined in step h., enables independent calculation of retardance entered to both said out-of-plane and said in-plane orthogonal components of a beam of electromagnetic radiation by each of said converging input and diverging output lenses, and retardance entered by said sample system to said in-plane orthogonal component of said beam of electromagnetic radiation, at given wavelengths in said spectroscopic set of ellipsometric data.
As before for other parameter evaluation steps, the step h. simultaneous evaluation of parameters in said mathematical model parameterized equations for said in-plane retardation entered by said parameterized sample system, and said converging input and diverging output lenses, is typically achieved by a square error reducing mathematical curve fitting procedure.
If the sample system present can not be easily parameterized, the presently disclosed method of accurately evaluating parameters in parameterized equations in a mathematical model of a system of spatially separated input converging and diverging output lenses, provides that the following steps, g.-j. be practiced:
g. removing the sample system from said means for supporting a sample system positioned between said converging input and diverging output lenses, and positioning in its place an alternative sample system for which a parameterized equation for calculating in-plane retardance entered to a beam of electromagnetic radiation, given wavelength, can be provided;
h. providing a parameterized equation for retardation entered in-plane to an orthogonal component of a beam of electromagnetic radiation by said alternative sample system which is then positioned on said means for supporting a sample system positioned between said converging input and diverging output lenses, and as necessary similar parameterized equations for retardation entered by each of said input converging and diverging output lenses to the in-plane orthogonal component of a beam of electromagnetic radiation;
i. obtaining a spectroscopic set of ellipsometric data with said alternative sample system present on the means for supporting a sample system, utilizing a beam of electromagnetic radiation provided by said source of electromagnetic radiation, said beam of electromagnetic radiation being caused to pass through said converging input lens, interact with said alternative sample system in a plane of incidence thereto, and exit through said diverging output lens and enter said detector system;
j. by utilizing said parameterized mathematical model for said converging input lens and said diverging output lens provided in step d. and said parameterized equation for retardation entered by said alternative sample system provided in step h., and said spectroscopic set of ellipsometric data obtained in step i., simultaneously evaluating parameters in said mathematical model parameterized equations for independent calculation of retardance entered to an in-plane orthogonal component of said beam of electromagnetic radiation by said alternative sample system and by said converging input lens and said diverging output lens, such that correlation between DELTA""S entered by said alternative sample system and retardance entered by said in-plane orthogonal component of said beam of electromagnetic radiation, by each of said converging input and diverging output lenses, at given wavelengths in said spectroscopic set of ellipsometric data, is broken, said simultaneous evaluation optionally providing new values for parameters in parameterized equations for calculation of retardance entered in said out-of-plane components of said beam of electromagnetic radiation by each of said converging input lens and said diverging output lens;
The end result being that application of said parameterized equations for each of said converging input lens and diverging output lens and alternative sample system, for each of which values of parameters therein have been determined in step j., enables independent calculation of retardance entered to both said out-of-plane and said in-plane orthogonal components of a beam of electromagnetic radiation by each of said input converging lens and said diverging output lens, and retardance entered by said alternative sample system to said in-plane orthogonal component of a beam of electromagnetic radiation, at given wavelengths in said spectroscopic set of ellipsometric data.
As before, said presently disclosed method of accurately evaluating parameters in parameterized equations in a mathematical model of a system of spatially separated input converging and diverging output lenses provides that in the step j. simultaneous evaluation of parameters in said mathematical model parameterized equations for said in-plane retardation entered by said parameterized sample system, and at least said in-plane input lens and diverging output lens, is typically achieved by a square error reducing mathematical curve fitting procedure.
As mentioned with respect to the first method of the present invention disclosed herein, the presently disclosed method of accurately evaluating parameters in parameterized equations in a mathematical model of a system of spatially separated input converging and diverging output lenses provides that the step b. positioning of an ellipsometer system source of electromagnetic radiation and an ellipsometer system detector system includes positioning a polarizer between said source of electromagnetic radiation and said converging input lens, and the positioning of an analyzer between said diverging output lens and said detector system, and in which the step e. obtaining of a spectroscopic set of ellipsometric data involves obtaining data at a plurality of settings of at least one component selected from the group consisting of: (said analyzer and said polarizer). As well, it is again to be understood that additional elements can also be placed between said source of electromagnetic radiation and said converging input lens, and/or between said diverging output lens and said detector system, and that the step e. obtaining of a spectroscopic set of ellipsometric data can involve, alternatively or in addition to the recited procedure, obtaining data at a plurality of settings of at least one of said additional components.
Said presently disclosed method of accurately evaluating parameters in parameterized equations in a mathematical model of a system of spatially separated converging input and diverging output lenses also provides that the step of providing separate parameterized mathematical model parameterized equations for enabling independent calculation of out-of-plane and in-plane retardance entered by said converging input said diverging output lenses to said beam of electromagnetic radiation caused to pass through said input and diverging output lenses, and that retardance entered by a parameterized sample system, involve parameterized equations having a form selected from the group consisting of:
ret(xcex)=(K1/xcex)
ret(xcex)=(K1/xcex)*(1+(K2/xcex2))
ret(xcex)=(K1/xcex)*(1+(K2/xcex2)+(K3/xcex4))
It is again noted that while the present invention can be practiced with any type xe2x80x9clensesxe2x80x9d, be there one or two of them, (ie. one of the input or diverging output lenses can be essentially non-birefringent and even ambient), and while an converging input lens or diverging output lens can be considered to be a compoiste formed by a plurality of elements, (eg. a compensator and a polarizer), the step a. providing of spatially separated converging input and diverging output lenses is best exemplified as being practiced by the providing of an ellipsometer system that has both converging input and diverging output lenses present therein through which an beam of electromagnetic radiation is caused to enter and exit, repectively.
Any method of the present invention can further involve, in a functional order the following steps a1.-a4:
a1. fixing evaluated parameter values in mathematical model parameterized equations, for each of said converging input lens and diverging output lens, such that said parameterized equations allow independent determination of retardation entered between orthogonal components of a beam of electromagnetic radiation caused to pass through said converging input and diverging output lenses, given wavelength; and
a2. causing an unknown sample system to be present on said means for supporting a sample system;
a3. obtaining a spectroscopic set of ellipsometric data with said unknown sample system present on the means for supporting a sample system, utilizing a beam of electromagnetic radiation provided by said source of electromagnetic radiation, said beam of electromagnetic radiation being caused to pass through said converging input lens, interact with said alternative sample system in a plane of incidence thereto, and exit through said diverging output lens and enter said detector system; and
a4. by utilizing said mathematical model for said input converging lens and said diverging output lens in which parameter values in mathematical model parameterized equations, for each of said converging input lens and diverging output lens have been fixed, simultaneously evaluating PSI""S and uncorrelated DELTA""S parameters for said unknown sample system.
As in other steps in the present invention method in which parameter values are evaluated, it is again noted that the method of accurately evaluating parameters in parameterized equations in a mathematical model of a system of spatially separated input converging and diverging output lenses in which said simultaneous evaluation of PSI""S and DELTA""S for said unknown sample are typically achieved by a square error reducing mathematical curve fitting procedure.
As alluded to earlier, the step of providing spatially separated converging input and diverging output lenses, at least one of said converging input and diverging output lenses demonstrating birefringence when a beam of electromagnetic radiation is caused to pass therethrough, can involve one lens is not birefringent. And, said one lens which is not birefringent can be essentially a surrounding ambient, (ie. a phantom lens which is essentially just the atmosphere surrounding a sample system).
It is noted that where parameters in parameterized equations for out-of-plane retardance equations have been determined, a focused version of the present invention method for accurately evaluating parameters in parameterized equations in a mathematical model of a system of spatially separated input converging and diverging output lenses can comprise the steps of b1-b7:
b1. fixing evaluated parameter values in mathematical model parameterized equations, for each of said converging input lens and diverging output lens, such that said parameterized equations allow independent determination of retardation entered between orthogonal components of a beam of electromagnetic radiation caused to pass through said converging input and diverging output lenses, given wavelength; and
b2. causing an unknown sample system to be present on said means for supporting a sample system;
b3. obtaining a spectroscopic set of ellipsometric data with said unknown sample system present on the means for supporting a sample system, utilizing a beam of electromagnetic radiation provided by said source of electromagnetic radiation, said beam of electromagnetic radiation being caused to pass through said converging input lens, interact with said alternative sample system in a plane of incidence thereto, and exit through said diverging output lens and enter said detector system; and
b4. by utilizing said mathematical model for said input converging lens and said diverging output lens in which parameter values in mathematical model parameterized equations, for each of said converging input lens and diverging output lens have been fixed, simultaneously evaluating ALPHA""S and BETA""S for said unknown sample system;
b5. applying transfer functions to said simultaneously evaluated ALPHA""S and BETA""S for said unknown sample system to the end that a data set of effective PSI""s and DELTA""s for a combination of said lenses and said sample system is provided;
b6. providing a mathematical model for said combination of said lenses and said sample system which separately accounts for the retardation effects of the presence of said lenses and said sample system by parameterized equations; and
b7. by utilizing said mathematical model for said combination of said lenses and said sample system which separately accounts for the effects of the presence of at least said lenses by parameterized equations; and said data set of effective PSI""s and DELTA""s for a combination of said lenses and said sample system, simultaneously evaluating actual PSI""s and DELTA""s for said unknown sample system per se.
In the case, for instance, where the ellipsometer involved is a Rotating Analyzer, or Rotating Polarizer ellipsometer system, (but not where the ellipsometer involved is a Rotating Compensator System), it is noted that determination of xe2x80x9chandednessxe2x80x9d is required. Therefore the foregoing method can include, as necessary, providing a mathematical model for said combination of said lenses and said sample system which separately accounts for the retardation effects of the presence of said lenses and said sample system by parameterized equations which further includes providing for the effects of handedness. It is specifically stated that where the present invention approach of regressing onto effective PSI and DELTA values, (as determined in step b7.), is utilized, the mathematical modle can be derived so that xe2x80x9chandednessxe2x80x9d is accounted for in arriving at actual PSI""s and DELTA""s for said unknown sample system per se.
As a general comment it is to be understood that separate PSI and DELTA values are achieved for each angle of incidence a beam of electromagnetic radiation makes with respect to a sample substrate and for each wavelength utilized in a spectroscopic range of wavelengths.
It is noted that the terminology xe2x80x9cConverging Inputxe2x80x9d and xe2x80x9cDiverging Outputxe2x80x9d used throughout this Specification and Claims refers to the effect an Input Lens or Output Lens has on a beam of electromagnetic radiation. Ideally said language should be replaced with xe2x80x9cInput Lens Assemblyxe2x80x9d and xe2x80x9cOutput Lens Assemblyxe2x80x9d respectfully.
The present invention will be better understood by reference to the Detailed Description Section of this Disclosure, with appropriate reference being has to the Drawings.
It is a primary objective and/or purpose of the present invention to describe a system which enables practice of focused beam small-spot spectroscopic ellipsometry over a large wavelength range, includeing into the deep UV, (eg. wavelengths down to and below 190 NM). Multi-element lenses which comrpise elements made of different materials allow essentially the same focal length to be achieved over a wavelength range.
It is another primary objective and/or purpose of the present invention to provide methods, (as originally presented in co-pending application Ser. No. 09/162,217 as regards compensating Vacuum Window Birefringence), for essentially eliminating birefringence achromatic effects of multiple element input and output lenses, (optionally in combination with other ellipsometrically indistinguishable elements), in the analysis of ellipsometric data obtained utilizing an ellipsometer system beam of electromagnetic radiation which passes through said lenses.